Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 6 x + 75 x^{2} + 271 x^{3} + 1725 x^{4} + 3174 x^{5} + 12167 x^{6}$ |
| Frobenius angles: | $\pm0.482438368000$, $\pm0.572555853001$, $\pm0.650258719525$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.409383800271.1 |
| Galois group: | $S_4\times C_2$ |
| Cyclic group of points: | yes |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $17419$ | $183195623$ | $1754282191636$ | $21809170902953551$ | $266917134741022140944$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $30$ | $644$ | $11847$ | $278492$ | $6443145$ | $148040633$ | $3404771652$ | $78311069828$ | $1801151362317$ | $41426513903699$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobian of 1 hyperelliptic curve, but it is unknown how many Jacobians of non-hyperelliptic curves it contains:
- $y^2=22 x^8+7 x^7+2 x^6+3 x^5+9 x^4+18 x^3+3 x^2+20 x+13$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$| The endomorphism algebra of this simple isogeny class is 6.0.409383800271.1. |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 3.23.ag_cx_akl | $2$ | (not in LMFDB) |